Could fibromyalgia cause muscle fatigue?

Not fatigue alone. Not unless you have the other symptoms of fibromyalgia as well. If you are simply in poor condition that is a more likely cause for your complaint.
Yes, change it. Diet is the key when it comes to beating fatigue and fibromyalgia. Eliminating sugars and high carb foods (grains, lentils based foods) helps to reduce inflammation. Consuming vegetables, eggs, flesh foods, olive oil, saturated fats (butter) help fight it. take a vitmain D3 and probiotic supplement daily.